(4) Activity measured by α rays: long time of exposure,
The equations for the α rays for any time of exposure can be readily deduced, but the expressions are somewhat complicated.
Fig. 91.
225. Equations of rise of excited activity. The curves expressing the gradual increase to a maximum of the excited activity produced on a body exposed in the presence of a constant amount of emanation are complementary to the curves of decay for a long exposure. The sum of the ordinates of the rise and decay curves is at any time a constant. This follows necessarily from the theory and can also be deduced simply from à priori considerations. (See [section 200].)
The curves of rise and decay of the excited activity for both the α and β rays are shown graphically in [Fig. 91]. The thick line curves are for the α rays. The difference between the shapes of the decay curves when measured by the α or β rays is clearly brought out in the figure. The equations representing the rise of activity to a maximum are given below.
For the β and γ rays,
